On Permutation Polynomials Over Finite Fields

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Abstract

A polynomial f over a finite field F is called a permutation polynomial if the mapping F → F defined by f is one-to-one. In this paper we consider the problem of characterizing permutation polynomials; that is, we seek conditions on the coefficients of a polynomial which are necessary and sufficient for it to represent a permutation. We also give some results bearing on a conjecture of Carlitz which says essentially that for any even integer m, the cardinality of finite fields admitting permutation polynomials of degreem is bounded. © 1987, Hindawi Publishing Corporation. All rights reserved.

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Mollin, R. A., Small, C., Mollin, R. A., & Small, C. (1987). On Permutation Polynomials Over Finite Fields. International Journal of Mathematics and Mathematical Sciences, 10(3), 535–543. https://doi.org/10.1155/S0161171287000644

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